Whole-arm tactile feedback is crucial for robots to ensure safe physical interaction with their surroundings. This paper introduces CushSense, a fabric-based soft and stretchable tactile-sensing skin designed for physical human-robot interaction (pHRI) tasks such as robotic caregiving. Using stretchable fabric and hyper-elastic polymer, CushSense identifies contacts by monitoring capacitive changes due to skin deformation. CushSense is cost-effective ($\sim$US\$7 per taxel) and easy to fabricate. We detail the sensor design and fabrication process and perform characterization, highlighting its high sensing accuracy (relative error of 0.58%) and durability (0.054% accuracy drop after 1000 interactions). We also present a user study underscoring its perceived safety and comfort for the assistive task of limb manipulation. We open source all sensor-related resources on https://emprise.cs.cornell.edu/cushsense.